The open-access problem in fisheries: A fishery is characterized by the following growth rate: g(S)=100S-S2 , where S is the stock of fish (in tons). The market price of fish is P. The amount of fish caught per unit of effort is proportional to the size of the fish population. That is, q=kS, where q is the quantity caught per unit of effort, and k some constant. Note that the catch is equal to Q=qE, where E is the effort. Effort, by the way, is increasingly costly to exert the total extraction cost is rising at an increasing rate: TC=0.5E2 . For simplicity, assume P=1 and k=1 unless otherwise noted.

a. What is the surplus at the optimal sustainable catch?

b. If the fishery is in open-access, what will be the exerted effort, i.e. Ec?

c. What is the surplus under open-access? What is the welfare loss associated with openaccess?

d. How do the optimal and open-access catches (answers in d. and e.) change with a change in the price of fish P? Provide a quantitative relationship between changes in E* and Ec as P varies